Question

A conical pit of top diameter $3.5\mathrm{m}$ is $12\mathrm{m}$ deep.

What is its capacity in $\mathrm{kilolitres}$?

Answer 1

Find the capacity of the pit.

Given: Diameter $=3.5\mathrm{m}$ and Height $\mathrm{h}=12\mathrm{m}$

So, radius of pit $\mathrm{r}=1.75\mathrm{m}$ ; [Radius is half of diameter]

Capacity of pit $=$Volume of cone (pit)

$\Rightarrow$ $=\frac{1}{3}{\mathrm{\pi r}}^2\mathrm{h}$

$\Rightarrow$ $=\frac{1}{3}\left(\frac{22}{7}\right){\left(1.75\right)}^2\left(12\right)$ ; $\left[\because \mathrm{\pi }=\frac{22}{7}\right]$

$\Rightarrow$ $=38.5{\mathrm{m}}^3$

$\Rightarrow$ $=38.5{\mathrm{kl}}^3$ ; $\left[\because 1{\mathrm{m}}^3=1{\mathrm{kl}}^3\right]$

Hence, the capacity of the conical pit is $38.5$ kiloliters.